Discrete structure of van der Waals domains in globular proteins

Most globular proteins are divisible by domains, distinct substructuresof the globule. The notion of hierarchy of the domains was introducedearlier via van der Waals energy profiles that allow one tosubdivide the proteins into domains (subdomains). The questionremains open as to what is the possible structural connectionof the energy profiles. The recent discovery of the loop-n-lockelements in the globular proteins suggests such a structuralconnection. A direct comparison of the segmentation by van derWaals energy criteria with the maps of the locked loops of nearlystandard size reveals a striking correlation: domains in generalappear to consist of one to several such loops. In addition,it was demonstrated that a variety of subdivisions of the sameprotein into domains is just a regrouping of the loop-n-lockelements.     

Conformational modeling of substrate binding to endocellulase E2 from Thermomonospora fusca

Molecular mechanics calculations have been used to place a cellotetraosesubstrate into the active site of the crystallographlcally determinedstructure of endocellulase E2 from Thermomonospora fusca. Inthe lowest energy model structure, the second residue of thesubstrate oligosaccharide is tilted away from the planar ribbongeometry of cellulose as it is in the X–ray structureof the E2_cd–cellobiose cocrystal. This tilt is the resultof the topology of the binding site, and results in severalstrong carbohydrate–protein hydrogen bonds. The tiltingproduces a twisting of the glycosidic linkage of the cleavagesite between residues two and three. In the predicted enzyme–substratecomplex both of the Asp residues believed to function in generalacid and base roles in the previously proposed model for themechanism are distant from the bond being cleaved. Moleculardynamics simulations of the complex were conducted, and whilethe putative catalytic Asp residues remained distant from thecleavage site, the proton of Tyr73 briefly came within van derWaals contact of the linkage oxygen.     

Calculation of van der Waals forces in adhering systems

The existing theories of van der Waals attractive forces between two media separated by a vacuum or a third medium can be adapted to the case of true adhesion by introducing an adjustable parameter z₀. The consistency of the new model leads to the introduction of an effective dielectric constant. A study of the influence of the frequency range of the dielectric spectrum on van der Waals forces shows that when there is adhesion or when the intermediate layer is thin, only the u.v. component of the dielectric spectrum plays a role.The invariance of van der Waals forces to changes in the i.r. component of the dielectric spectrum allows the work function of electrons and accordingly the always and simultaneously present electrostatic adhesion forces, which are of the same order of magnitude, to be varied without changing the magnitude of the van der Waals adhesion forces.     

Energetic analysis of binding of progesterone and 5{beta}-androstane-3,17-dione to anti-progesterone antibody DB3 using molecular dynamics and free energy calculations

Molecular dynamics simulations and molecular mechanics–Poisson–Boltzmannsurface area (MM-PBSA) free energy calculations were used tostudy the energetics of the binding of progesterone (PRG) and5ß-androstane-3,17-dione (5AD) to anti-PRG antibodyDB3. Although the two steroids bind to DB3 in different orientations,their binding affinities are of the same magnitude, 1 nM forPRG and 8 nM for 5AD. The calculated relative binding free energyof the steroids, 8.8 kJ/mol, is in fair agreement with the experimentalenergy, 5.4 kJ/mol. In addition, computational alanine scanningwas applied to study the role of selected amino acid residuesof the ligand-binding site on the steroid cross-reactivity.The electrostatic and van der Waals components of the totalbinding free energies were found to favour more the bindingof PRG, whereas solvation energies were more favourable forthe binding of 5AD. The differences in the free energy componentsare due to the binding of the A rings of the steroids to differentbinding pockets: PRG is bound to a pocket in which electrostaticantibody–steroid interactions are dominating, whereas5AD is bound to a pocket in which van der Waals and hydrophobicinteractions dominate.     

Characterisation of inter-particle forces within agglomerated metallurgical powders

The strength of agglomerates of nickel flash furnace concentrate and dust was determined from experimental observations of agglomerates forming under controlled conditions, combined with mathematical equations from the literature. It was found that the agglomerates had a tensile strength ranging from 0.01 Pa to 38.7 Pa, while inter-particle forces ranged from 2.2 × 10^− 12 N to 1.5 × 10^− 10 N. These values were compared to the expected magnitude of van der Waals, electrostatic, magnetic and capillary forces within the agglomerates, and it was found that both electrostatic and van der Waals forces are likely to contribute to the cohesion of agglomerates, although sub-micron particles and the presence of sufficiently large asperities on the surface of particles limit the magnitude of van der Waals forces. Magnetic forces are large enough to contribute to the cohesion of dust agglomerates, which is in keeping with the high magnetite content of the recycle dust. It is postulated that electrostatic forces, acting over a longer range than van der Waals forces, may be responsible for initially bringing particles together. The methodology for determining inter-particle forces can be applied to the computer modelling of flash smelting systems, as well as other gas/particle systems such as fluidized beds.     

Role of Interfacial Interactions in the Deposition of Colloidal Clay Particles in Porous Media

Colloidal clay particle transport under saturated conditions is believed to be controlled by its interactions with the surrounding environment. The dominating forces among these interactions are electrostatic forces that are determined by colloidal clay particle and porous medium surface charge density and Lifshitz–van der Waals forces that are determined by colloidal clay particle and porous medium surface thermodynamic properties. Electrostatic forces are greatly affected by solution chemistry in terms of solution ionic strength and pH. In this research, electrostatic and Lifshitz–van der Waals forces of natural colloidal clay particles with a model porous medium of silica sand were quantified at different ionic strength and pH conditions. At the same time, colloidal clay particle transport in the model medium of silica sand was conducted in a laboratory column. The maximum electrostatic forces, F ^EL (max), which occurred when the separation distance between colloidal clay particles and the porous medium was in the range of the sum of the double layer thicknesses of the colloidal clay particles and the porous medium, was found to be the determinant factor for colloidal clay particle deposition in the porous medium. Colloidal clay particle desorption in the porous media was related to the net effect of attractive Lifshitz–van der Waals forces and repulsive electrostatic forces, evaluated at the equilibrium distance where physical contact between the colloidal clay particle and silica sand actually occurred (i.e., affix force). Higher colloidal clay particle desorption was found to coincide with smaller affix force values.     

Theoretical analysis of colloidal interaction energy in nanoparticle suspensions

This study is focused on understanding interaction energies for Al₂O₃ nanoparticle suspensions at high solids loadings. Among the four interaction energies: van der Waals interaction energy, electrostatic interaction energy, steric interaction energy, and depletion interaction energy, the study found that the van der Waals attraction is the dominant mechanism in destabilizing the dispersion system; the steric repulsion is a more effective stabilization mechanism than the electrostatic repulsion. The fundamental cause for an unstable suspension due to the particle–particle close contact and thus attraction at high solids loading can be overcome by increasing the particle–particle repulsion. When a dispersant is used in a suspension, the polymer chain length must be carefully selected so that the dispersant provides enough stabilization but does not compromise the maximum achievable solids loading. If an appropriate dispersant is chosen, up to 45 vol% solids loading suspension can be obtained for the Al₂O₃ nanoparticles.     

Dielectric Anisotropy and the van der Waals Interaction between Bulk Media

We derive the van der Waals interaction energy between two semi-infinite dielectrically anisotropic bodies acting across a planar slab filled with a third anisotropic material. The derivation, valid in the non-retarded limit, is performed by a summation of electromagnetic surface-mode fluctuations. The result is a free energy of interaction as a function of body separation and of rotation of the various media. The angular dependence of the energy predicts a torque between the two bodies; in some cases the van der Waals interaction between like substances will change from attraction to repulsion under rotation.     

Dielectric Anisotropy and the van der Waals Interaction between Bulk Media

We derive the van der Waals interaction energy between two semi-infinite dielectrically anisotropic bodies acting across a planar slab filled with a third anisotropic material. The derivation, valid in the non-retarded limit, is performed by a summation of electromagnetic surface-mode fluctuations. The result is a free energy of interaction as a function of body separation and of rotation of the various media. The angular dependence of the energy predicts a torque between the two bodies; in some cases the van der Waals interaction between like substances will change from attraction to repulsion under rotation.     

Exploring forces between individual colloidal particles with the atomic force microscope

Forces between individual colloidal particles can be measured with the atomic force microscope (AFM), and this technique permits the study of interactions between surfaces across aqueous solutions in great detail. The most relevant forces are described by the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, and they include electrostatic double-layer and van der Waals forces. In symmetric systems, the electrostatic forces are repulsive and depend strongly on the type and concentration of the salts present, while van der Waals forces are always attractive. In asymmetric systems, the electrostatic force can become attractive as well, even when involving neutral surfaces, while in rare situations van der Waals forces can become repulsive too. The enormous sensitivity of the double layer forces on additives present is illustrated with oppositely charged polyelectrolytes, which may induce attractions or repulsions depending on their concentrations.     

A population balance model for flocculation of colloidal suspensions by polymer bridging

A detailed population balance model for flocculation of colloidal suspensions by polymer bridging under quiescent flow conditions is presented. The collision efficiency factor is estimated as a function of interaction forces between polymer coated particles. The total interaction energy is computed as a sum of van der Waals attraction, electrical double layer repulsion and bridging attraction or steric repulsion due to adsorbed polymer. The scaling theory is used to compute the forces due to adsorbed polymer and the van der Waals attraction is modified to account for presence of polymer layer around a particle. The irregular structure of flocs is taken into account by incorporating the mass fractal dimension of flocs. When tested with experimental floc size distribution data published in the literature, the model predicts the experimental behavior adequately. This is the first attempt towards incorporating theories of polymer-induced surface forces into a flocculation model, and as such the model presented here is more general than those proposed previously.     

Effects of Electrostatic and van der Waals Interactions on the Adhesion of Spherical 7µm Particles

The force needed to detach spherical particles having a number average diameter of 7.1 μm from a polymeric, photoconducting substrate was determined by ultracentrifugation. In the absence of any release agents applied to the substrate, it was found that only a small fraction of the particles could be removed from the substrate even at the highest centripetal accelerations (354,000 g). However, when the substrate was coated with a thin layer of a release aid (zinc stearate), the force needed to separate the particles from the substrate was greatly reduced, thereby allowing the detachment force to be determined. Under these conditions, it was found that the release force varied with the square of the particle charge-to-mass ratio. Moreover, it was also found by extrapolation that the detachment force at zero charge, corresponding to the residual van der Waals interactions, was finite. These results suggest that both van der Waals and electrostatic interactions affect the adhesion of particles and, for micrometer-sized particles, electrostatic forces can become dominant under some circumstances. Conversely, the large increase in the adhesion of the particles to the substrate, in the absence of a good release agent, suggests that van der Waals forces would often dominate adhesive interactions of particles in this size range.     

Recent Results in Particle Adhesion: UHV Measurements, Light-Modulated Adhesion and the Effect of Adsorbates

In the past few years, the force of adhesion F between small metal spheres (about 2 to 8 μm in diameter) and flat semiconducting or metallic substrates has been measured under a variety of conditions. Most of this work has been or is about to be published. This is a summarizing review of the results obtained. An ultracentrifuge technique has been employed. In measurements under ultra-high vacuum the adhesion between Au spheres and flat Si substrates was studied as a function of the oxide layer thickness on Si. Also flat Au substrates were used. The results fit with the Lifshitz theory of van der Waals forces. In another series of measurements the van der Waals component F_ndW of F was separated from the electrostatic one F_el which originates from the electrostatic double layer formed at the interface of the adherents. This was achieved by varying F_el by band-gap light of varying intensity. The adherents were Zr-coated Au spheres on CdS.     

The effects of non-continuum hydrodynamics on the Brownian coagulation of aerosol particles

Most theoretical predictions of the rate of Brownian-induced coagulation have considered the continuum hydrodynamic resistance of the suspending gas or liquid as well as van der Waals and/or electrostatic forces. However, the mean-free path of the gas is comparable with the length scale at which van der Waals forces become important during the collision of two Brownian aerosol particles. We predict the initial rate of coagulation in a monodisperse aerosol driven by Brownian motion in the presence of van der Waals forces and non-continuum lubrication forces when the Knudsen number (ratio of the mean-free path to the particle radius) is small but non-zero. A comparison with experiments demonstrates the accuracy of the predictions and the importance of accounting for non-continuum effects to provide quantitative predictions of coagulation rates.     

Capillary and van der Waals force between microparticles with different sizes in humid air

It is well known that surface effect forces, such as van der Waals force and capillary force, are the major contributions to adhesion when microsized particles are in contact in humid environment. But it is very complex to calculate the adhesion force between two smooth unequal particles. In conventional approaches, the effective particle radius approximation and the constant half-filling angle assumptions are often used for computing the van der Waals forces between two microparticles. However, the approximation and the assumption are actually difficult to accurately model the forces between unequal particle sizes when the surfaces are with different properties. In this paper, we present a theoretical study of the van der Waals force and capillary force between two microparticles with different radii and the surface properties linked by a liquid bridge. The proposed model provides the adhesion force predictions in good agreement with the previous formula and existing experiment data. Considering the solid particles are partially wetted by the liquid bridge, the van der Waals force is calculated by divided the particle surface into a wetted part and a dry portion in our stimulation. Since the wetted surface portion of the particle is determined by the half-filling angle, the relationship between two half-filling angles of the unequal size particles is developed from the geometrical consideration, which is relate to the size ratio of the particles, the contact angle, and the separation distance. Then, the van der Waals force is determined using the surface element integration. Moreover, the influences of humidity, particles size, contact angle, and separation distance toward the adhesion forces are discussed using the proposed method. Simulations indicate that a higher relative humidity leads to bigger liquid bridges, suggesting a higher capillary force, but at the same time, the van der Waals force decreases due to the decrease in surfaces energy. As for the influence of contact angle, results show that a higher contact angle, that is, a more hydrophobic surface, reduces the capillary force but increases the van der Waals force (absolute value). The simulations also show that the both the capillary force and the van der Waals force (absolute value) increase as the particle size increases. When the particles are separated from each other, the capillary force and van der Waals force decreases gradually. These results are helpful to understand and utilize the adhesion interaction between particles with unequal sizes at the ambient condition.     

Use of a minimum perturbation approach to predict TIM mutant structures

A minimum perturbation conformational search approach is usedto model the structures of the yeast triosephosphate isomerase(TIM) single mutant in which the catalytic base Glul65 is changedto Asp, and the double mutant in which Glul65 is changed toAsp and Ser96 to Pro. In chicken TIM this double mutant is referredto as a pseudo–revertant because some of the catalyticactivity lost due to the first mutation is regained when thesecond mutation occurs. Three minimum energy structures werecalculated for the Asp 165 conformation in the yeast TEM singlemutant and another three for the double mutant One of the calculatedminimum energy conformations for Aspl65 in the E165D structureagrees well with the X–ray structure. However, this conformationis not that of the lowest energy and is not one of the threemost common conformers for Asp found by Ponder and Richards.This suggests that when an amino acid is introduced it may notbe able to conform to the more general rules that apply to proteinstructures of evolutionary origin. While the van der Waals energylargely determines the allowed minima, the relative rankingof the final minima is determined by electrostatic effects andcan therefore be affected by the inclusion of crystal watersin the calculation. When the E165D calculation is repeated withan active–site water molecule fixed in its E165D X–raystructure position, the relative ranking of the minima shiftsand the X–ray conformation for Asp 165 is the lowest interactionenergy conformer. Two of the E165D calculated minimum energystructures are essentially identical to two of the S96P/E165Dminima. All of the calculated minima for both the E165D andS96P/E165D mutants position the Asp side chain such that theanti–orbital, and not the more basic syn–orbital,of the carboxylate would be utilized for proton abstraction.This observation may explain why the chicken TIM S96P/E165Dmutant, for which the X-ray structure indicates that the syn–orbitalis used, is a pseudo–revertant while the yeast TIM doublemutant is not; no X–ray structure is available for thelatter. The multiplicity of minima found in the present analysismakes clear that predicting the exact orientation of a singleside chain is not as simple as might be expected.     

Repulsive van der Waals Forces. II. Mechanism of Hydrophobic Chromatography

Abstract

When two materials with different interfacial free energies are immersed in a liquid with an interfacial free energy intermediate between those of the two materials, the net van der Waals forces between these two materials are repulsive. Thus by lowering the interfacial free energy of the liquid medium, solutes or particles previously adsorbed onto low energy surfaces can be readily eluted from such surfaces. This is demonstrated by the coupling to and subsequent elution from Octyl Sepharose and Phenyl Sepharose of serum and other proteins. The elution of all proteins commenced when the surface tension of the eluting liquid was decreased to a point just below that of the protein in question. The eluted serum proteins successively emerged from the column in the exact decreasing order of their own interfacial free energies. In hydrophobic chromatography, coupling is favored when the van der Waals forces between solutes (or particles) and ligand are attractive (and maximum, frequently through the admixture of salts); elution is brought about by causing the van der Waals interaction between each solute (or particle) and ligand successively to become repulsive (by gradually lowering the surface tension of the eluting liquid).     

修正的van der Waals模型及其对液相流体的应用

用7种代表性物质在广阔温度和压力范围内的液体物性实验值，对两个不同程度上修正的van der Waals模型进行比较和评价。结果表明，从统计力学出发，进一步张Lennard-Jones位能函数对内压项进行修正的van der Waals模型，较仅对已占体积项进行修正的van der Waals模型明显更成。     

Determination of three-dimensional structures of proteins by simulated annealing with interproton distance restraints. Application to crambin, potato carboxypeptidase inhibitor and barley serine proteinase inhibitor 2

An automated method, based on the principle of simulated annealing,is presented for determining the three-dimensional structuresof proteins on the basis of short (<5 Å) interprotondistance data derived from nuclear Overhauser enhancement (NOE)measurements. The method makes use of Newton's equations ofmotion to increase temporarily the temperature of the systemin order to search for the global minimum region of a targetfunction comprising purely geometric restraints. These consistof interproton distances supplemented by bond lengths, bondangles, planes and soft van der Waals repulsion terms. The latterreplace the dihedral, van der Waals, electrostatic and hydrogen-bondingpotentials of the empirical energy function used in moleculardynamics simulations. The method presented involves the implementationof a number of innovations over our previous restrained moleculardynamics approach [Clore,G.M., Brünger,A.T., Karplus,M.and Gronenborn,A.M. (1986) J. Mol. Biol., 191, 523–551].These include the development of a new effective potential forthe interproton distance restraints whose functional form isdependent on the magnitude of the difference between calculatedand target values, and the design and implementation of robustand fully automatic protocol. The method is tested on threesystems: the model system crambin (46 residues) using X-raystructure derived interproton distance restraints, and potatocarboxypeptidase inhibitor (CPI; 39 residues) and barley serineproteinase inhibitor 2 (BSPI-2; 64 residues) using experimentallyderived interproton distance restraints. Calculations were carriedout starting from the extended strands which had atomic r.m.s.differences of 57, 38 and 33 Å with respect to the crystalstructures of BSPI-2, crambin and CPI respectively. Unbiasedsampling of the conformational space consistent with the restraintswas achieved by varying the random number seed used to assignthe initial velocities. This ensures that the different trajectoriesdiverge during the early stages of the simulations and onlyconverge later as more and more interproton distance restraintsare satisfied. The average backbone atomic r.m.s. differencebetween the converged structures is 2.2 ± 0.3 Åfor crambin (nine structures), 2.4 ± 0.3 Å forCPI (eight structures) and 2.5 ± 0.2 Å for BSPI-2(five structures). The backbone atomic r.m.s. difference betweenthe mean structures derived by averaging the coordinates ofthe converged structures and the corresponding X-ray structuresis 1.2 Å for crambin, 1.6 Å for CPI and 1.7 Åfor BSPI-2.     

The effect of air on the packing structure of fine particles

A numerical study of the effect of air on the packing structure of fine particles has been performed by a combined continuum and discrete numerical model. The forces considered are gravity, contact force, drag force, and van der Waals forces. The results are analyzed in terms of particle rearrangement, local porosity, coordination number, radial distribution function, and the distribution of contact forces. The results indicate the degree to which drag and van der Waals forces promote mean porosity increases and mean coordination number decreases. Drag forces allow contacts of particles reaching a state of rest in a packing to be closer to the Coulomb failure criterion for shear displacement when van der Waals forces are small. Increasing van der Waals forces imposes contact conditions that are far away from the Coulomb failure criterion. Increased drag and van der Waals forces tends to lead to more heterogeneous structure. It is demonstrated that average normal contact force is related to the ratio of van der Waals forces to particle weight.